Reddy A.

asked • 09/01/19

Prove or Disprove this statement

There exists a prime number x such that x + 16 and x + 32 are also prime numbers

1 Expert Answer

By:

Sam Z. answered • 09/01/19

Math/Science Tutor

Al P.

tutor
21 is not prime
Report

09/24/19

Al P.

tutor
Disproved: if x is prime, x mod 3 must be 1 or 2. But (x + 16) mod 3 is then 2 or 0 respectively, and (x+32) mod 3 is 0 or 1, respectively. Thus, one of { x, x+16, x+32 } is always divisible by 3 and therefore at least one of the three numbers is composite.
Report

09/24/19

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.